Showing papers on "Parametric oscillator published in 2013"

Parametric resonance in tunable superconducting cavities

Abstract: We develop a theory of parametric resonance in tunable superconducting cavities. The nonlinearity introduced by the superconducting quantum interference device (SQUID) attached to the cavity and damping due to connection of the cavity to a transmission line are taken into consideration. We study in detail the nonlinear classical dynamics of the cavity field below and above the parametric threshold for the degenerate parametric resonance, featuring regimes of multistability and parametric radiation. We investigate the phase-sensitive amplification of external signals on resonance, as well as amplification of detuned signals, and relate the amplifier performance to that of linear parametric amplifiers. We also discuss applications of the device for dispersive qubit readout. Beyond the classical response of the cavity, we investigate small quantum fluctuations around the amplified classical signals. We evaluate the noise power spectrum both for the internal field in the cavity and the output field. Other quantum-statistical properties of the noise are addressed such as squeezing spectra, second-order coherence, and two-mode entanglement.

Design and characterization of a lumped element single-ended superconducting microwave parametric amplifier with on-chip flux bias line

Abstract: We demonstrate a lumped-element Josephson parametric amplifier, using a single-ended design that includes an on-chip, high-bandwidth flux bias line. The amplifier can be pumped into its region of parametric gain through either the input port or through the flux bias line. Broadband amplification is achieved at a tunable frequency ω/2π between 5 and 7 GHz with quantum-limited noise performance, a gain-bandwidth product greater than 500 MHz, and an input saturation power in excess of −120 dBm. The bias line allows fast frequency tuning of the amplifier, with variations of hundreds of MHz over time scales shorter than 10 ns.

Squeezing with a flux-driven Josephson parametric amplifier

Abstract: Josephson parametric amplifiers (JPA) are promising devices for applications in circuit quantum electrodynamics and for studies on propagating quantum microwaves because of their good noise performance. In this work, we present a systematic characterization of a flux-driven JPA at millikelvin temperatures. In particular, we study in detail its squeezing properties by two different detection techniques. With the homodyne setup, we observe the squeezing of vacuum fluctuations by superposing signal and idler bands. For a quantitative analysis, we apply dual-path cross-correlation techniques to reconstruct the Wigner functions of various squeezed vacuum and thermal states. At 10?dB signal gain, we find 4.9???0.2?dB squeezing below the vacuum. In addition, we discuss the physics behind squeezed coherent microwave fields. Finally, we analyze the JPA noise temperature in the degenerate mode and find a value smaller than the standard quantum limit for phase-insensitive amplifiers.

Fiber optical parametric oscillator for coherent anti-Stokes Raman scattering microscopy

Abstract: We present a synchronously pumped fiber optical parametric oscillator for coherent anti-Stokes Raman scattering microscopy. Pulses from a 1 μm Yb-doped fiber laser are amplified and frequency converted to 779-808 nm through normal dispersion four-wave mixing in a photonic crystal fiber. The idler frequency is resonant in the oscillator cavity, and we find that bandpass filtering the feedback is essential for stable, narrow-bandwidth output. Experimental results agree quite well with numerical simulations of the device. Transform-limited 2 ps pulses with energy up to 4 nJ can be generated at the signal wavelength. The average power is 180 mW, and the relative-intensity noise is much lower than that of a similar parametric amplifier. High-quality coherent Raman images of mouse tissues recorded with this source are presented.

Design and characterization of a lumped element single-ended superconducting microwave parametric amplifier with on-chip flux bias line

Abstract: We demonstrate a lumped-element Josephson parametric amplifier, using a single-ended design that includes an on-chip, high-bandwidth flux bias line. The amplifier can be pumped into its region of parametric gain through either the input port or through the flux bias line. Broadband amplification is achieved at a tunable frequency $\omega/2 \pi$ between 5 to 7 GHz with quantum-limited noise performance, a gain-bandwidth product greater than 500 MHz, and an input saturation power in excess of -120 dBm. The bias line allows fast frequency tuning of the amplifier, with variations of hundreds of MHz over time scales shorter than 10 ns.

Generation of 120 GW mid-infrared pulses from a widely tunable noncollinear optical parametric amplifier

Abstract: We demonstrate a noncollinear optical parametric chirped-pulse amplification scheme for generating high-peak-power tunable mid-infrared (IR) pulses. The high-gain LiNbO3-based noncollinear parametric amplifier, seeded by a tunable femtosecond optical parametric amplifier, provides a wide wavelength tuning range from 3.3 to 3.95 μm and a large saturated gain of over 4000 in a single-stage amplifier. The compressed mid-IR pulse has a pulse energy of 13.3 mJ and pulse duration of 111 fs, with a peak power as high as 120 GW. To the best of our knowledge, this is the highest peak power ever reported for 3–5 μm tunable mid-IR lasers.

Parametrically excited MEMS vibration energy harvesters with design approaches to overcome the initiation threshold amplitude

Abstract: Resonant-based vibration harvesters have conventionally relied upon accessing the fundamental mode of directly excited resonance to maximize the conversion efficiency of mechanical-to-electrical power transduction. This paper explores the use of parametric resonance, which unlike the former, the resonant-induced amplitude growth, is not limited by linear damping and wherein can potentially offer higher and broader nonlinear peaks. A numerical model has been constructed to demonstrate the potential improvements over the convention. Despite the promising potential, a damping-dependent initiation threshold amplitude has to be attained prior to accessing this alternative resonant phenomenon. Design approaches have been explored to passively reduce this initiation threshold. Furthermore, three representative MEMS designs were fabricated with both 25 and 10 ?m thick device silicon. The devices include electrostatic cantilever-based harvesters, with and without the additional design modification to overcome initiation threshold amplitude. The optimum performance was recorded for the 25 ?m thick threshold-aided MEMS prototype with device volume ?0.147?mm3. When driven at 4.2?ms?2, this prototype demonstrated a peak power output of 10.7 nW at the fundamental mode of resonance and 156 nW at the principal parametric resonance, as well as a 23-fold decrease in initiation threshold over the purely parametric prototype. An approximate doubling of the half-power bandwidth was also observed for the parametrically excited scenario.

Global stabilization of high-energy response for a Duffing-type wideband nonlinear energy harvester via self-excitation and entrainment:

Abstract: This article presents a resonance-type vibration energy harvester with a Duffing-type nonlinear oscillator that can perform effectively in a wide frequency range. To mitigate the power-bandwidth trade-off in conventional linear harvesters, the resonance frequency band of the harvester is expanded by introducing a Duffing-type nonlinear oscillator in order to enable the harvester to generate larger electric power in a wider frequency range. Such a nonlinear oscillator, however, can have multiple stable steady-state responses in the resonance band with different levels of regeneration energy. In this study, the principle of self-excitation is utilized to destabilize the solutions, except for the highest energy solution. A load circuit with a switch between the conventional load circuit and a negative resistance circuit and the switching control law, which depends on the amplitude of the oscillator’s response, are introduced to impart the self-excitation capability in order to entrain the oscillator with the...

A dispersive nanoSQUID magnetometer for ultra-low noise, high bandwidth flux detection

Abstract: We describe a dispersive nanoSQUID (nanoscale superconducting quantum interference device) magnetometer comprised of two variable thickness aluminum weak-link Josephson junctions shunted in parallel with an on-chip capacitor. This arrangement forms a nonlinear oscillator with a tunable 4–8 GHz resonant frequency with a quality factor Q = 30 when coupled directly to a 50 Ω transmission line. In the presence of a near-resonant microwave carrier signal, a low frequency flux input generates sidebands that are readily detected using microwave reflectometry. If the carrier excitation is sufficiently strong, then the magnetometer also exhibits parametric gain, resulting in a minimum effective flux noise of 30 nΦ0 Hz−1/2 with 20 MHz of instantaneous bandwidth. If the magnetometer is followed with a near-quantum-noise-limited Josephson parametric amplifier, we can increase the bandwidth to 60 MHz without compromising sensitivity. This combination of high sensitivity and wide bandwidth with no on-chip dissipation makes this device ideal for local sensing of spin dynamics, both classical and quantum.

Dynamics of the N-pendulum and its application to a wave energy converter concept

Abstract: This paper considers a design of an N-pendulum, which represents a special case of a physical pendulum. The design of the N-pendulum not only allows uncoupling the natural frequency of the pendulum from its length, but also provides easy control of the frequency and torque. The proposed design is stimulated by the idea of developing a wave power take-off system based on the parametric pendulum. Different designs are being considered and their dynamic characteristics are investigated with respect to the feasibility of such an application. Due to the observed low frequency of ocean waves, the size of a heaving simple pendulum should span along unrealistic sizes in order to be parametrically resonant. Thus, the N-pendulum is considered and the configurations that would fulfill these frequency requirements are sought. Last, numerical simulation is conducted for an under development experimental rig aiming to test the functionality of the concept, modelling the response of the N-pendulum.

Stability analysis and numerical confirmation in parametric resonance of axially moving viscoelastic plates with time-dependent speed

Abstract: In this paper, stability in parametric resonance of axially moving viscoelastic plates subjected to plane stresses is investigated. The plate material obeys the Kelvin–Voigt model in which the material time derivative is used. The generalized Hamilton principle is employed to obtain the governing equation. The axial speed is characterized as a simple harmonic variation about the constant mean speed. The governing equation can be regarded as a continuous gyroscopic system with small periodically parametric excitations and a damping term. The method of multiple scales is applied to the governing equation to establish the solvability conditions in principal and summation parametric resonances. The natural frequencies and modes of linear generating equation are numerically calculated based on the given boundary conditions. The necessary and sufficient condition of the stability is derived from the Routh–Hurwitz criterion. Some numerical examples are presented to demonstrate the effects of related parameters on the frequencies and the stability boundaries. The differential quadrature scheme is developed to solve numerically the linear generating system and the primitive equation model. The numerical calculations confirm the analytical results.

Investigation of nonlinear effects in Josephson parametric oscillators used in circuit QED

Abstract: We experimentally study the behavior of a parametrically pumped nonlinear oscillator, which is based on a superconducting λ/4 resonator, and is terminated by a flux-tunable SQUID. We extract parameters for two devices. In particular, we study the effect of the nonlinearities in the system and compare to theory. The Duffing nonlinearity,α, is determined from the probe-power dependent frequency shift of the oscillator, and the nonlinearity, β, related to the parametric flux pumping, is determined from the pump amplitude for the onset of parametric oscillations. Both nonlinearities depend on the parameters of the device and can be tuned in-situ by the applied dc flux. We also suggest how to cancel the effect of β by adding a small dc flux and a pump tone at twice the pump frequency.

Oscillators and Oscillator Systems: Classification, Analysis and Synthesis

Abstract: Preface. 1. Introduction. 2. Fundamentals of oscillator design. 3. Classification of oscillators. 4. Noise in oscillators. 5. Noise in first-order oscillators. 6. Noise in second-order oscillators. 7. Oscillator tuning. 8. Oscillator systems. About the authors. Index.

Investigation of nonlinear effects in Josephson parametric oscillators used in circuit quantum electrodynamics

Abstract: We experimentally study the behavior of a parametrically pumped nonlinear oscillator, which is based on a superconducting λ/4 resonator, and is terminated by a flux-tunable superconducting quantum interference device. We extract parameters for two devices. In particular, we study the effect of the nonlinearities in the system and compare to theory. The Duffing nonlinearity, α, is determined from the probe-power dependent frequency shift of the oscillator, and the nonlinearity, β, related to the parametric flux pumping, is determined from the pump amplitude for the onset of parametric oscillations. Both nonlinearities depend on the parameters of the device and can be tuned in situ by the applied dc flux. We also suggest how to cancel the effect of β by adding a small dc flux and a pump tone at twice the pump frequency.

Squeezing with a flux-driven Josephson parametric amplifier

Abstract: Josephson parametric amplifiers (JPA) are promising devices for applications in circuit quantum electrodynamics (QED) and for studies on propagating quantum microwaves because of their good noise performance. In this work, we present a systematic characterization of a flux-driven JPA at millikelvin temperatures. In particular, we study in detail its squeezing properties by two different detection techniques. With the homodyne setup, we observe squeezing of vacuum fluctuations by superposing signal and idler bands. For a quantitative analysis we apply dual-path cross-correlation techniques to reconstruct the Wigner functions of various squeezed vacuum and thermal states. At 10 dB signal gain, we find 4.9+-0.2 dB squeezing below vacuum. In addition, we discuss the physics behind squeezed coherent microwave fields. Finally, we analyze the JPA noise temperature in the degenerate mode and find a value smaller than the standard quantum limit for phase-insensitive amplifiers.

Periodic and chaotic responses of an axially accelerating viscoelastic beam under two-frequency excitations

Abstract: This study focuses on the steady-state periodic response and the chaotic behavior in the transverse motion of an axially moving viscoelastic tensioned beam with two-frequency excitations. The two-frequency excitations come from the external harmonic excitation and the parametric excitation from harmonic fluctuations of the moving speed. A dynamic model is established to include the finite axial support rigidity, the material derivative in the viscoelastic constitution relation, and the longitudinally varying tension due to the axial acceleration. The derived nonlinear integro-partial-differential equation of motion possesses space-dependent coefficients. Applying the differential quadrature method (DQM) and the integral quadrature method (IQM) to the equation of the transverse motion, a set of nonlinear ordinary differential equations is obtained. Based on the Runge–Kutta time discretization, the time history of the axially moving beam is numerically solved for the case of the primary resonance, the super–harmonic resonance, and the principal parametric resonance. For the first time, the nonlinear dynamics is studied under various relations between the forcing frequency and the parametric frequency, such as equal, multiple, and incommensurable relationships. The stable periodic response and its sensitivity to initial conditions are determined using the bidirectional frequency sweep. Furthermore, chaotic motions are identified using different methods including the Poincare map, the maximum Lyapunov exponent, the fast Fourier transforms, and the initial value sensitivity. Numerical simulations reveal the characteristics of the periodic, quasiperiodic, and chaotic motion of a nonlinear axially moving beam under two-frequency excitations.

Handedness control in a 2-μm optical vortex parametric oscillator

Abstract: We present the first handedness control of an optical vortex output from a vortex-pumped optical parametric oscillator. The handedness of the optical vortex was identical to that of the pump vortex beam. Over 2 mJ, 2-μm optical vortex with a topological charge of ± 1 was achieved. We found that the handedness of a fractional vortex with a half integer topological charge can also be selectively controlled.

Multi-frequency Operation of a MEMS Vibration Energy Harvester by Accessing Five Orders of Parametric Resonance

Abstract: The mechanical amplification effect of parametric resonance has the potential to outperform direct resonance by over an order of magnitude in terms of power output. However, the excitation must first overcome the damping-dependent initiation threshold amplitude prior to accessing this more profitable region. In addition to activating the principal (1st order) parametric resonance at twice the natural frequency ?0, higher orders of parametric resonance may be accessed when the excitation frequency is in the vicinity of 2?0/n for integer n. Together with the passive design approaches previously developed to reduce the initiation threshold to access the principal parametric resonance, vacuum packaging (< 10 torr) is employed to further reduce the threshold and unveil the higher orders. A vacuum packaged MEMS electrostatic harvester (0.278 mm3) exhibited 4 and 5 parametric resonance peaks at room pressure and vacuum respectively when scanned up to 10 g. At 5.1 ms?2, a peak power output of 20.8 nW and 166 nW is recorded for direct and principal parametric resonance respectively at atmospheric pressure; while a peak power output of 60.9 nW and 324 nW is observed for the respective resonant peaks in vacuum. Additionally, unlike direct resonance, the operational frequency bandwidth of parametric resonance broadens with lower damping.

Suppression of spin-exchange relaxation using pulsed parametric resonance.

Abstract: We demonstrate that spin-exchange dephasing of Larmor precession at near-Earth-scale fields is effectively eliminated by dressing the alkali-metal atom spins in a sequence of ac-coupled $2\ensuremath{\pi}$ pulses, repeated at the Larmor precession frequency. The contribution of spin-exchange collisions to the spectroscopic linewidth is reduced by a factor of the duty cycle of the pulses. We experimentally demonstrate resonant transverse pumping in magnetic fields as high as 0.1 G, present experimental measurements of the suppressed spin-exchange relaxation, and show enhanced magnetometer response relative to a light-narrowed scalar magnetometer.

A Practical Quantum-Limited Parametric Amplifier Based on the Josephson Ring Modulator

Abstract: A Practical Quantum-Limited Parametric Amplifier Based on the Josephson Ring Modulator Flavius Dietrich Octavian Schackert 2013 This dissertation has addressed the problem of developing the Josephson Parametric Converter (JPC) as a practical phase-preserving microwave parametric amplifier operating at the quantum limit of added noise. The device consists of two superconducting resonators coupled through the Josephson Ring Modulator (JRM), which in essence consists of a loop of four identical Josephson tunnel junctions, threaded by an applied magnetic flux. The nonlinearity of the JRM is of the tri-linear form XY Z without spurious nonlinear terms and involving only the minimal number of modes, thus placing the JPC close to the ideal non-degenerate parametric amplifier. This pure form of the nonlinearity is confirmed here by the observation of coherent attenuation (CA), the time-reversed process of three-wave parametric amplification, with signal, idler, and pump modes in the fully nonlinear regime. The design developed in this dissertation allows fabrication of the amplifier in a single lithography step, greatly simplifying parameter adjustments from one device to the next. Measured device characteristics and amplifier performances are presented, and limitations linked to the junction energy EJ and the circuit parameters discussed. The use of these JPCs in the readout of superconducting qubits is shown to lead to almost ideal quantum measurements, as the measurement efficiency can approach the ideal value of 1. A Practical Quantum-Limited Parametric Amplifier Based on the Josephson Ring Modulator A Dissertation Presented to the Faculty of the Graduate School of Yale University in Candidacy for the Degree of Doctor of Philosophy by Flavius Dietrich Octavian Schackert Dissertation Director: Professor Michel H. Devoret December 2013 Copyright c © 2013 by Flavius Dietrich Octavian Schackert All rights reserved.

A quadratic-shaped-finger comb parametric resonator

Abstract: A large-stroke (8 µm) parametric resonator excited by an in-plane 'shaped-finger' electrostatic comb drive is fabricated using a 15 µm thick silicon-on-insulator microelectromechanical systems (SOI-MEMS) process. A quadratic capacitance-engagement response is synthesized by engineering a custom-shaped comb finger profile. A folded-flexure suspension allows lateral motion while constraining rotational modes. The excitation of the nonlinear parametric resonance is realized by selecting an appropriate combination of the linear and cubic electrostatic stiffness coefficients through a specific varying-gap comb-finger design. The large-amplitude parametric resonance promotes high signal-to-noise ratio for potential use in sensitive chemical gravimetric sensors, strain gauges, and mode-matched gyroscope applications.

Band structure in the polymer quantization of the harmonic oscillator

Abstract: We discuss the detailed structure of the spectrum of the Hamiltonian for the polymerized harmonic oscillator and compare it with the spectrum in the standard quantization. As we will see the non-separability of the Hilbert space implies that the point spectrum consists of bands similar to the ones appearing in the treatment of periodic potentials. This feature of the spectrum of the polymeric harmonic oscillator may be relevant for the discussion of the polymer quantization of the scalar field and may have interesting consequences for the statistical mechanics of these models.

The pumpistor: A linearized model of a flux-pumped superconducting quantum interference device for use as a negative-resistance parametric amplifier

Abstract: We describe a circuit model for a flux-driven Superconducting QUantum Interference Device (SQUID). This is useful for developing insight into how these devices perform as active elements in parametric amplifiers. The key concept is that frequency mixing in a flux-pumped SQUID allows for the appearance of an effective negative resistance. In the three-wave, degenerate case treated here, a negative resistance appears only over a certain range of allowed input signal phase. This model readily lends itself to testable predictions of more complicated circuits.

Three-wave mixing with three incoming waves: signal-idler coherent attenuation and gain enhancement in a parametric amplifier.

Abstract: We demonstrate the time-reversed process of nondegenerate three-wave parametric amplification from three distinct sources in the fully nonlinear regime using a Josephson amplifier. In the reverse process, coherent attenuation, signal and idler beams destructively interfere in the presence of a pump to generate additional pump photons. This effect is observed through the symmetric phase-dependent amplification and attenuation of the signal and idler beams and, in the depleted pump regime, through the phase-dependent modulation of the amplifier gain, directly probing the enhancement of the pump. Results are found to be in good agreement with theory.

Continuous-wave, two-crystal, singly-resonant optical parametric oscillator: theory and experiment.

Abstract: We present theoretical and experimental study of a continuous-wave, two-crystal, singly-resonant optical parametric oscillator (T-SRO) comprising two identical 30-mm-long crystals of MgO:sPPLT in a four- mirror ring cavity and pumped with two separate pump beams in the green. The idler beam after each crystal is completely out-coupled, while the signal radiation is resonant inside the cavity. Solving the coupled amplitude equations under undepleted pump approximation, we calculate the maximum threshold reduction, parametric gain acceptance bandwidth and closest possible attainable wavelength separation in arbitrary dual-wavelength generation and compare with the experimental results. Although the T-SRO has two identical crystals, the acceptance bandwidth of the device is equal to that of a single-crystal SRO. Due to the division of pump power in two crystals, the T-SRO can handle higher total pump power while lowering crystal damage risk and thermal effects. We also experimentally verify the high power performance of such scheme, providing a total output power of 6.5 W for 16.2 W of green power at 532 nm. We verified coherent energy coupling between the intra-cavity resonant signal waves resulting Raman spectral lines. Based on the T-SRO scheme, we also report a new technique to measure the temperature acceptance bandwidth of the single-pass parametric amplifier across the OPO tuning range.

Parametric Excitation in a Two Degree of Freedom MEMS System

Abstract: This contribution investigates the influence of parametric excitation on the dynamic stability of a microelectrome- chanical system. In systems with just a single degree of freedom, parametric excitation causes the oscillator to exhibit unstable behavior within certain intervals of the parametric excitation frequency. In multi-degree of freedom systems on the other hand, unstable behavior is caused within a wider range of intervals of the parametric excitation frequency. Moreover, such systems show frequency intervals of enhanced stability, an effect known as anti-resonance phenomenon. Both types of phenomena, the parametric resonance and anti-resonance, are modeled and studied for a microelectromechanical system with two degrees of freedom and some novel results are discussed.